Parabolic Differential Inequalities in Cones

ResearchCommons/Manakin Repository

Parabolic Differential Inequalities in Cones

Show full item record

Title: Parabolic Differential Inequalities in Cones
Author: Vaughn, Randy; Lakshmikantham, V.
Abstract: In this paper we investigate the theory of parabolic differential inequalities in arbitrary cones. After discussing the fundamental results concerning parabolic inequalities in cones, we prove a result on flow-invariance which is then used to obtain a comparison theorem. This comparison result is useful in deriving upper and lower bounds on solutions of parabolic differential equations in terms of the solutions of ordinary differential equations. We treat the Dirichlet problem in this paper since its theory follows the general pattern of ordinary differential equations and requires less restrictive assumptions. The treatment of Neumann problem, on the other hand, demands stronger smoothness assumptions and depends heavily on strong maximum principle. The study of the corresponding results relative to Newmann problem is discussed elsewhere.
Date: 1978-03

Files in this item

Files Size Format View Description
MathTechReport078.pdf 604.2Kb PDF View/Open PDF

This item appears in the following Collection(s)

Show full item record


My Account


About Us